Moment-based dimension reduction for multivariate response regression

Dimension reduction aims to reduce the complexity of a regression without requiring a pre-specified model. In the case of multivariate response regressions, covariance-based estimation methods for the kth moment-based dimension reduction subspaces circumvent slicing and nonparametric estimation so that they are readily applicable to multivariate regression settings. In this article, the covariance-based method developed by Yin and Cook (2002. J. Roy. Statist. Soc. Ser. B 64, 159-175) for univariate regressions is extended to multivariate response regressions and a new method is proposed. Simulated and real data examples illustrating the theory are presented.